论文标题
适当的正交分解降低汉堡方程的订单模型的均匀界限和差异的商
Uniform Bounds with Difference Quotients for Proper Orthogonal Decomposition Reduced Order Models of the Burgers Equation
论文作者
论文摘要
在本文中，我们证明了汉堡方程的正确正交分解（POD）减少订单建模（ROM）的统一误差范围，考虑了[26]中引入的差异商（DQS）。特别是，我们通过考虑$ l^2（ω）$和$ h^1_0（ω）$ pod空间以及$ l^{\ infty}（l^2）$和自然 - norm错误来研究DQ ROM误差的行为。我们提供了一些有意义的数值测试，以检查误差界的行为。基于我们的数值结果，DQ ROM错误是小于NODQ的几个数量级（其中POD以标准方式构造，即，即没有DQ方法），根据ROM基础所保留的能量。此外，NODQ ROM错误具有最佳行为，而DQ ROM错误（将DQ添加到POD过程中）表明了最佳/超级示威行为。据推测，这可能是因为DQ内部产品允许ROM空间中的时间依赖性产生影响。
In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in [26]. In particular, we study the behavior of the DQ ROM error bounds by considering $L^2(Ω)$ and $H^1_0(Ω)$ POD spaces and $l^{\infty}(L^2)$ and natural-norm errors. We present some meaningful numerical tests checking the behavior of error bounds. Based on our numerical results, DQ ROM errors are several orders of magnitude smaller than noDQ ones (in which the POD is constructed in a standard way, i.e., without the DQ approach) in terms of the energy kept by the ROM basis. Further, noDQ ROM errors have an optimal behavior, while DQ ROM errors, where the DQ is added to the POD process, demonstrate an optimality/super-optimality behavior. It is conjectured that this possibly occurs because the DQ inner products allow the time dependency in the ROM spaces to make an impact.
